This is a bit of a different question. First of all, it's worth noting that religion and politics are the two conversational topic that will almost inevitably lead to an argument. It's extremely difficult to debate these topics, because each person feels so strongly about their view being the correct one. So, I guess my first tip would be, don't. Rather than debating who is right and who is wrong, talk about your own beliefs, why you believe that, how it makes you feel, or your own experiences. In other words, talk about your own beliefs, not another person's.
My second tip would be, don't enter a conversation with the goal of converting someone to your own point of view unless that person has asked you to do so. Many atheists, and even some theists, are ready and willing to listen to different points of view regarding God (which God you are referring to is unclear). If you want to explain your point of view, or your interpretation of God, I think most people are happy to listen. It's only when you preach, or try to influence another person's view of God (or lake there-of) that you will run into retaliation or being tuned out.
Thirdly, if you are going to enter a conversation, and talk to a non-believer about God, it's important to listen, as well. A conversation involves two people, and both people must be involved in dialogue. One person yelling at the top of his or her lungs about any topic, drowning out the other person, is not a conversation. If this is what you find yourself doing when you approach the topic, then you are not being polite or considerate to the other person, and they are much less likely to give you a chance.
Also, it's important to actively listen to your discussion partner. It's not the same to just be thinking of your next retort when the other person is talking. If you're not hearing what is being said, then it is just as bad as if you were yelling non-stop. It's certainly not productive or respectful.
Lastly, understand that the world is made up of billions of people, and every person is unique. We don't all believe the same things, speak the same language, think the same, or have the same likes and dislikes. Not everyone is going to agree with you. Some people might not even listen to you because they haven't learned how to have a conversation yet. Others, especially of a minority religion or non-belief system, may feel like you are trying to lecture or demean them, which is not a pleasant feeling.